In Revenge of the Sith, Yoda and Obi-Wan split up to confront Palpatine and Skywalker in single-combat. However, with the millions of lives at stake, and the obvious power of the Emperor with his immense skill in the force, and the massive armies at his disposal, wouldn't it have been better and safer to confront Palpatine together? With Anakin on a mission to Mustafar, he wouldn't be around to help Palpatine, and can be dealt with later.
This is especially so given that Mace Windu, widely regarded as the best swordsman of the era, whose Vaapad fighting style draws on the Darkness of the opponent and becomes even more effective against a Sith, attempted Palpatine's arrrest with two other accomplished Jedi Masters.
Yoda and Obi-Wan are also affiliated with the light side of the force and shouldn't be as susceptible to raw emotions like pride. In this sense, Palpatine appears surprisingly accurate when he tells Yoda that "Your arrogance blinds you".